Least Common Multiple (LCM) of 101 and 145
The least common multiple (LCM) of 101 and 145 is 14645.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 101 and 145?
First, calculate the GCD of 101 and 145 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 145 = 0 remainder 101 |
| 2 | 145 ÷ 101 = 1 remainder 44 |
| 3 | 101 ÷ 44 = 2 remainder 13 |
| 4 | 44 ÷ 13 = 3 remainder 5 |
| 5 | 13 ÷ 5 = 2 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 25 | 550 |
| 158 and 127 | 20066 |
| 151 and 126 | 19026 |
| 148 and 89 | 13172 |
| 70 and 168 | 840 |